A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels

Abstract

A test for the rank of a vector error correction model (VECM) or panel VECM based on the well-known trace test is proposed. The proposed test employs instrumental variables (IV's) generated by a class of nonlinear functions of the estimated stochastic trends of the VECM under the null. The test improves on the standard trace test by replacing the non-standard critical values with chi-squared critical values. Extending the result to the panel VECM case, the test is robust to cross-sectional correlation of the disturbances. The nonlinear IV rank test also extends earlier research on nonlinear IV unit root tests. However, the optimal instrument in the univariate case is not admissible in the more general multivariate case. The chi-squared result suggests that IV tests may be used to replace limits of other standard tests with integrated time series that are given by nonstandard stochastic integrals, even without a panel with which to pool test statistics.